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{'Lhash': '1580811595582459603494048560646,1600109348441641210702706005395,2250385232461989996021486681797', 'a10': 0, 'a2': 1, 'a3': -9, 'a4': -8, 'a5': 0, 'a6': -9, 'a7': 16, 'a8': -12, 'a9': 54, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 115334.71800677532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 9, 27, 27]], [5, [1]], [11, [1, -33, 363, -1331]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, -1, 9, -5, 72, -64, 512], [1, 9, 27, 27], [1], [1, -16, 856, -11150, 293608, -1882384, 40353607], [1, -33, 363, -1331], [1, -45, 6871, -192794, 15095587, -217206405, 10604499373], [1, 58, 15434, 572224, 75827242, 1399979002, 118587876497], [1, 169, 28098, 2360147, 192724182, 7950753889, 322687697779], [1, -155, 41944, -3812131, 510332648, -22945562795, 1801152661463], [1, 277, 68543, 12078682, 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'2.97029458858689015338525211300653', '3.23054795752020912331568928382217', '3.96320387692851659190594900196297', '4.10040012031390303175985092269456', '4.22345054335914501648876979700884', '4.73523686464525354459439630887975', '4.94185744590564265955608826779546', '4.98944415978559613841897480701674', '5.68899766698085835265853581391427', '5.95008204989237871528680858802512', '6.02987606153651054039243844245319', '6.47012140906186325521478136930516', '6.55932097755422708933437199250016', '7.17278476585545262622482414383686', '7.21397965371771272436779538667092', '7.73926583350674272645103976608871', '7.80966644406917050810989327776177', '8.622194468202238909872669325818644', '8.664123869522520366132567728920505', '8.702915205585140090904192747814091', '9.263293876261939526661978520544648', '9.415944008943847658113461369511567', '9.437606378960605265936717953703568'], 'prelabel': '6-825e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151063, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 1919424546645415407, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24704046627505110969373102320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.26226370906427648111550413283', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.77524093157596250946077326926', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 115334.71800677532, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, 1, -9, -8, 0, -9, 16, -12, 54, 0, 33, 72, 45, 16, 0, -7, -58, 54, -169, 0, -144, 33, 155, 108, 0, 45, -270, -128, -277, 0, -173, 53, -297, -58, 0, -432, 60, -169, -405, 0, 44, -144, -109, -264, 0, 155, 270, 63, -600, 0, 522, -360, -148, -270, 0, -192, 1521, -277, -684, 0, -1038, -173, 864, 184, 0, -297, 314, 464, -1395, 0, -1459, -648, -1170, 60, 0, 1352, 528, -405, -506, 0, 1215, 44, -347, 1152, 0, -109, 2493, -396, -607, 0, 720, -1240, 1557, 270, 0, -477, 1263, -600, 1782, 0], 'euler11': [1, -33, 363, -1331, 0, 0, 0], 'euler13': [1, -45, 6871, -192794, 15095587, -217206405, 10604499373], 'euler17': [1, 58, 15434, 572224, 75827242, 1399979002, 118587876497], 'euler19': [1, 169, 28098, 2360147, 192724182, 7950753889, 322687697779], 'euler2': [1, -1, 9, -5, 72, -64, 512], 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123002252493626, 119851595982618319], [1, 347, 1599297, 390027914, 914457233739, 113448309559043, 186940255267540403], [1, 607, 1367067, 593095898, 963739855923, 301667643613327, 350356403707485209], [1, -1263, 3146554, -2315882599, 2871774878842, -1052043642225327, 760231058654565217]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/a/q'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-825e3-1.1-c3e3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-825e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151063, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 1919424546645415407, 'z1': {'__RealLiteral__': 0, 'data': '1.24704046627505110969373102320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1580811595582459603494048560646,1600109348441641210702706005395,2250385232461989996021486681797', 'Lhash_array': ['1580811595582459603494048560646', '1600109348441641210702706005395', '2250385232461989996021486681797'], 'label': '6-825e3-1.1-c3e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/q'}